1. Field of the Invention
The present invention relates to a variable gain circuit and more particularly, to a variable gain circuit including a plurality of serially connected amplifier circuits, a phase compensation circuit, and a gain setting circuit.
2. Description of the Related Art
First, a constitution of a conventional variable gain circuit and its principle will be described. Here, FIG. 19 shows a schematic configuration of the conventional variable gain circuit.
A variable gain circuit 100 shown in FIG. 19 includes a differential amplifier circuit 110 to amplify an external input signal Vi, a feedback circuit 120 having two impedance elements Zs and Zf, gain controlling means 130 to set a gain value of the variable gain circuit 100, and a load capacity CL on the output side of the differential amplifier circuit 110.
The differential amplifier circuit 110 is composed of two amplifiers of a precedent stage amplifier DA1 and a subsequent stage amplifier DA2. According to the precedent stage amplifier DA1, the external input signal Vi is inputted to a positive side input terminal, and the impedance elements Zs and Zf of the feedback circuit 120 that will be described below are connected to a negative side input terminal. According to the subsequent amplifier DA2, an output terminal of the precedent stage amplifier DA1 is connected to an input terminal.
Since the differential amplifier circuit 110 shown in FIG. 19 is composed of the two amplifiers, it includes a phase compensation capacity Cc in order to ensure the stability of the circuit (refer to Gray Meyer et al., “Analysis and Design of Analog Integrated Circuits”, JOHN WILEY & SONS, pp. 624-680). According to the phase compensation capacity Cc, one end is connected to the output terminal of the subsequent stage amplifier DA2, and the other end is connected to the input terminal of the subsequent stage amplifier DA2, in which the capacity is variable.
The feedback circuit 120 forms a negative feedback loop with the impedance elements Zs and Zf. According to the impedance element Zf, one end is connected to the output terminal of the subsequent stage amplifier DA2, and the other end is connected to the negative side input terminal of the precedent stage amplifier DA1. In addition, according to the impedance element Zs, one end is connected to the other end of the impedance element Zf and the other end is grounded. The impedance elements Zs and Zf include a capacitative element, a resistor element, or combination of the capacitative element and the resistor element in general. Here, the values of the impedance elements Zs and Zf are variable.
Here, when the differential gain of the differential amplifier circuit 110 is sufficiently great, a variable gain G of an output signal Vo with respect to an input signal Vi is expressed by the following formula 1.
                              G          ≡                      Vo            Vi                          =                              Zf            Zs                    +          1                                    (        1        )            
As shown in the formula 1, according to the variable gain circuit 100, when the values of the impedance elements Zs and Zf are appropriately set, a gain value can be set.
According to the variable gain circuit 100 shown in FIG. 19, as a signal amount of the negative feedback of the feedback circuit 120 is increased, the stability of the circuit is lowered. A feedback factor F showing the degree of the stability of the circuit is expressed by the following formula 2.
                              F          ≡                      Zs                          Zf              +              Zs                                      =                  1          G                                    (        2        )            
As shown in the formula 2, the feedback factor F is designated by a ratio of the signal amount of the negative feedback of the feedback circuit 120 to a signal amount of the output signal Vo. As can be seen from the formula 2, as the value of the variable gain G is decreased, the feedback factor F is increased. That is, as the signal amount of the negative feedback is increased, the stability of the circuit is lowered.
In addition, when the value of the variable gain G is decreased, as a technique to keep the stability of the circuit, a variable gain circuit in which the capacity of the phase compensation capacity Cc is increased in conjunction with the decrease amount of the variable gain G is disclosed (refer to Japanese Patent Application Laid-Open No. 8-330868, for example, which is referred to as the patent document 1 hereinafter).
A description will be made of a relation between the variable gain G and the stability of the circuit with reference to FIGS. 20 and 21. Here, a phase margin is calculated from an open-loop transfer function in the negative feedback circuit.
Here, FIG. 20 shows a schematic circuit configuration when a negative feedback loop of the variable gain circuit (negative feedback circuit) shown in FIG. 19 is cut in order to provide the open-loop function. When it is assumed that a transfer function of the differential amplifier circuit 110 is H(s), the open-loop transfer function is expressed by a ratio of a voltage Vy of the negative feedback signal to a voltage difference Vid between the positive side input terminal and the negative side input terminal of the differential amplifier circuit 110, which is expressed by the following formula 3.
                              Vy          Vid                =                  F          ×                      H            ⁡                          (              s              )                                                          (        3        )            
Then, the transfer function H(s) of the differential amplifier circuit 110 is calculated. Here, FIG. 21 shows an equivalent circuit of the differential amplifier circuit 110 composed of the two amplifiers of the precedent stage amplifier DA1 and the subsequent stage amplifier DA2.
In addition, FIG. 21A shows an equivalent circuit of the precedent stage amplifier DA1, in which Gm1 represents a transconductance value, R1 represents an amplifier output resistor, C1 represents an amplifier load capacity, s represents a Laplace operator, and Vx represents an output signal. In addition, FIG. 21B shows an equivalent circuit of the subsequent stage amplifier DA2, in which Gm2 represents a transconductance value, and R2 represents an amplifier output resistor.
When the Kirchihoffs current law is applied to an output node of the precedent stage amplifier DA1 of the differential amplifier circuit 110, the following formula 4 is provided.
                                          Gm            ⁢                                                  ⁢            1            ×            Vid                    +                      Vx                          R              ⁢                                                          ⁢              1                                +                      Vx            ×            s            ×            C            ⁢                                                  ⁢            1                    -                      s            ×            Cc            ×            Vo                          =        0                            (        4        )            
In addition, when the Kirchihoffs current law is applied to an output node of the subsequent stage amplifier DA2 of the differential amplifier circuit 110, the following formula 5 is provided.
                                          Gm            ⁢                                                  ⁢            2            ×            Vx                    +                      Vo            ×            s            ×            Cc                    +                      Vo                          R              ⁢                                                          ⁢              2                                +                      Vo            ×            s            ×            CL                          =        0                            (        5        )            
The following formula 6 is provided from the formula 4 and the formula 5.
                                          H            ⁡                          (              s              )                                =                                    Vo              Vid                        ≈                          Adc                                                (                                      1                    +                                          s                                              ω                                                  P                          ⁢                                                                                                          ⁢                          1                                                                                                      )                                ×                                  (                                      1                    +                                          s                                              ω                                                  P                          ⁢                                                                                                          ⁢                          2                                                                                                      )                                                                    ⁢                                  ⁢                  Adc          =                      Gm            ⁢                                                  ⁢            1            ×            Gm            ⁢                                                  ⁢            2            ×            R            ⁢                                                  ⁢            1            ×            R            ⁢                                                  ⁢            2                          ⁢                                  ⁢                              ω                          P              ⁢                                                          ⁢              1                                =                      -                          1                              Gm                ⁢                                                                  ⁢                2                ×                R                ⁢                                                                  ⁢                1                ×                R                ⁢                                                                  ⁢                2                ×                Cc                                                    ⁢                                  ⁢                              ω                          P              ⁢                                                          ⁢              2                                =                                    -                                                Gm                  ⁢                                                                          ⁢                  2                                                  CL                  +                  Cc                                                      ×                          Cc                              C                ⁢                                                                  ⁢                1                                                                        (        6        )            
The following formula 7 is provided from the formula 3 and the formula 6.
                              F          ×                      H            ⁡                          (              s              )                                      ≈                              F            ×            Adc                                              (                              1                +                                  s                                      ω                                          P                      ⁢                                                                                          ⁢                      1                                                                                  )                        ×                          (                              1                +                                  s                                      ω                                          P                      ⁢                                                                                          ⁢                      2                                                                                  )                                                          (        7        )            
Here, when it is assumed that a frequency when the value of the open-loop transfer function F×H (s) is one is a unity frequency of ωU, in a case where a relation of ωP1<<ωU<<ωP2 is provided, the unity frequency ωU is calculated by the following formula 8.
                                          F            ×                          H              ⁡                              (                                  j                  ×                                      ω                    U                                                  )                                              ≈                                    F              ×              Adc                                                                                      j                  ×                                      ω                    U                                                                    ω                                      P                    ⁢                                                                                  ⁢                    1                                                                                                    =                  1          ⁢                                          ⁢                                    ω              U                        =                                          F                ×                Adc                ×                                  ω                                      P                    ⁢                                                                                  ⁢                    1                                                              =                              F                ×                                                      Gm                    ⁢                                                                                  ⁢                    1                                                        C                    ⁢                                                                                  ⁢                    c                                                                                                          (        8        )            
In addition, a relation s=j×ωU is provided in the formula 8. When it is assumed that s=j×ωU in the formula 7, the following formula 9 is provided.
                              F          ×                      H            ⁡                          (                              j                ×                                  ω                  U                                            )                                      =                                            F              ×              Adc                                                                                                                  (                                              1                        +                                                  j                          ×                                                                                    F                              ×                              Adc                              ×                                                              ω                                                                  P                                  ⁢                                                                                                                                          ⁢                                  1                                                                                                                                                    ω                                                              P                                ⁢                                                                                                                                  ⁢                                1                                                                                                                                                        )                                        ×                                                                                                                    (                                          1                      +                                              j                        ×                                                                              ω                            U                                                                                ω                                                          P                              ⁢                                                                                                                          ⁢                              2                                                                                                                                            )                                                                                ≈                      1                          j              ×                              (                                  1                  +                                                            ω                      U                                                              ω                                              P                        ⁢                                                                                                  ⁢                        2                                                                                            )                                                                        (        9        )            
According to the formula 9, a phase angle on the Gaussian plane in the case where the unity frequency ωU is provided is calculated by the following formula 10.
                              ∠          ⁢                                          ⁢          F          ×                      H            ⁡                          (                              j                ×                                  ω                  U                                            )                                      =                                            -              90                        ⁢            °                    -                                    tan                              -                1                                      ⁡                          (                                                ω                  U                                                  ω                                      P                    ⁢                                                                                  ⁢                    2                                                              )                                                          (        10        )            
Here, since the phase margin PM is defined by an angle allowance until a phase angle of the open-loop transfer function on the Gaussian plane when the unity frequency ωU is provided, that is, the phase angle represented by the formula 10 reaches −180 degrees, the following formula 11 is provided.
                                                                        -                180                            ⁢              °                        +                          P              ⁢                                                          ⁢              M                                =                                                    -                90                            ⁢              °                        -                                          tan                                  -                  1                                            ⁡                              (                                                      ω                    U                                                        ω                                          P                      ⁢                                                                                          ⁢                      2                                                                      )                                                    ⁢                                  ⁢                              P            ⁢                                                  ⁢            M                    =                                    90              ⁢              °                        -                                          tan                                  -                  1                                            ⁡                              (                                                      ω                    U                                                        ω                                          P                      ⁢                                                                                          ⁢                      2                                                                      )                                                                        (        11        )            
When ωP2 in the formula 6 and ωU in the formula 8 are assigned to the formula 11, the following formula 12 is provided.
                              P          ⁢                                          ⁢          M                =                              90            ⁢            °                    -                                    tan                              -                1                                      ⁡                          [                              F                ×                                                      Gm                    ⁢                                                                                  ⁢                    1                                                        Gm                    ⁢                                                                                  ⁢                    2                                                  ×                                  (                                                            CL                      Cc                                        +                    1                                    )                                ×                                                      C                    ⁢                                                                                  ⁢                    1                                    Cc                                            ]                                                          (        12        )            
As can be seen from the formula 12, the phase margin PM of the variable gain circuit composed of the plurality of stages of the amplifiers is monotonically decreased as the feedback factor F is increased. In other words, when the feedback factor F is increased, the stability of the variable gain circuit 100 could be damaged.
Therefore, according to the variable gain circuit disclosed in the above patent document 1, when the feedback factor F is increased, that is, when the variable gain G is decreased, the phase compensation capacity Cc is increased to keep the phase margin PM roughly constant, whereby the stability of the circuit is kept roughly constant.
However, according to the variable gain circuit disclosed in the above patent document 1, since it is necessary to increase the phase compensation capacity Cc in response to the increment of the variable gain G, it is necessary to provide the plurality of phase compensation capacities Cc.
Thus, for example, when the capacitative element is formed in an integrated circuit, the problem is that a chip area is increased and production cost becomes high because the plurality of phase compensation capacities Cc is provided. In addition, in a case of a discrete circuit, since it is necessary to mount a plurality of discrete components for the capacity, the problem is that the discrete circuit becomes large as a whole and a production cost becomes high.
Therefore, it is required to provide a variable gain circuit in which it is not necessary to provide a plurality of phase compensation capacities Cc while stability of a circuit is maintained regardless of a set variable gain G, and a production cost is lowered.